Edexcel Core Mathematics C4 June 2011

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C4 Mathematics Edexcel June 2011 Question 6

6. With respect to a fixed origin O, the lines l₁ and l₂ are given by the equations.
   where λ and μ are scalar parameters. (a) Show that l_l and l₂ meet and find the position vector of their point of intersection A.

(b) Find, to the nearest 0.1°, the acute angle between l₁ and l₂

The point B has position vector

(c) Show that B lies on l₁

(d) Find the shortest distance from B to the line l₂, giving your answer to 3 significant figures.

6. (a) Vectors

6. (b) Vectors

6. (c)

6. (d)

C4 Mathematics Edexcel June 2011 Question 7

Figure 3 shows part of the curve C with parametric equations
x = tanθ, y = sinθ , 0 ≤ θ < π/2

The point P lies on C and has coordinates (√3, ½√3)

(a) Find the value of ș at the point P.

The line l is a normal to C at P. The normal cuts the x-axis at the point Q.

(b) Show that Q has coordinates (k√3, 0) , giving the value of the constant k.

The finite shaded region S shown in Figure 3 is bounded by the curve C, the line x = √3 and the x-axis. This shaded region is rotated through 2π radians about the x-axis to form a solid of revolution.

(c) Find the volume of the solid of revolution, giving your answer in the form pπ√3 + qπ², where p and q are constants.

7. (a) Parametric equations

7. (b) Normal to a Parametric Curve

7. (c) Volume of Revolution to a Parametric Curve

C4 Mathematics Edexcel June 2011 Question 8

8. (a) Find ∫(4y + 3)^-1/2 dy

(b) Given that y =1.5 at x = – 2, solve the differential equation
dy/dx = √(4y + 3)/x²
giving your answer in the form y x = f(x).

8. (a) Integration methods

8. (b) Differential Equations

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